Force-matching Method Research Articles

Development of embedded-atom method (EAM) potential for Palladium–Barium alloy

ABSTRACT An embedded-atom method (EAM) potential for the Pd–Ba alloy system has been developed in order to forward computational research in this alloying system as there is no EAM potential available for this alloy system. The force-matching method has been implemented to develop the EAM potential first, and then, optimisation to converged density-functional theory (DFT) data sets has been done to generate the accurate and reliable potential for the Pd–Ba alloy system. Some physical, elastic and thermal properties of BaPd2 crystal have been calculated through molecular dynamics (MD) simulation using the developed EAM potential and then verified these properties with the help of DFT analysis in order to examine the performance of the potential. The presence of some even peaks of BaPd2 in virtual XRD spectra using MD simulation has been justified by DFT analysis. Slight deviations in melting points calculation at different compositions of the Pd–Ba alloy system have been observed. Higher Ba–Pd interaction using radial distribution characteristics and slower kinetics for inter-diffusion through diffusional characteristics study of BaPd2 have been reported using MD simulation with the developed EAM potential. In spite of some discrepancies due to deficiency in the potential, a closer agreement between MD and DFT analysis has been observed.

Predicting thermophysical properties of molten salts in the MgCl2-NaCl-KCl-LiCl system with a shell-model potential

Ternary eutectic salts composed of MgCl2, NaCl, and KCl, referred to as MNK salts, have recently emerged as promising candidates as high-temperature heat transfer fluids and thermal energy storage media. In this study, we performed classical molecular dynamics (MD) simulations to predict the densities, specific heat capacities, viscosities, and ionic self-diffusivities for MNK salts over a wide temperature range. The impact of LiCl additive on their thermophysical properties was also investigated. To capture the electronic polarization of Cl anions by neighboring cations, we developed a novel shell-model potential using the force-matching method and a dataset of ab initio calculated interatomic forces. Our extensive MD simulations predict structure and properties for pure salts and binary/ternary salt mixtures in the MgCl2-NaCl-KCl-LiCl system in overall good agreement with available experimental and theoretical data, which corroborates the accuracy and reliability of our developed potential.

Towards atomistic modelling of solid Pb-O formation and dissolution in liquid lead coolant: Interatomic potential development

Microscopic description of solid Pb-O formation and dissolution in liquid lead coolant is important for the modelling of fast neutron reactors. For this purpose, in this work we develop interatomic potential models for lead melt with dissolved oxygen. Potentials fitting is based on ab initio density functional theory (DFT) calculations and quantum molecular dynamics. Two different potential models are trained on the DFT data using the force-matching method: a computationally cheap embedded atom method (EAM) potential and a computationally expensive machine-learned moment tensor potential (MTP) that allows reproducing DFT data very accurately. The potentials are further validated to reproduce the properties of lead melt and the coordination of oxygen atoms in molten lead. The diffusion coefficient for oxygen in molten lead is calculated and compared with the available experimental data. We analyse how these interatomic potential models describe the crystal structure of the solid lead oxide to consider PbO nucleation and dissolution in molten lead. We extensively discuss the arising problems with the description of long-range electrostatic interactions. The possibility of matching the experimental data on the oxygen solubility limit by tuning the EAM potential is shown.

Angular dependent potential for Al-Zr binary system to study the initial heterogeneous nucleation behavior of liquid Al on L12-Al3Zr

A new binary Al-Zr angular dependent potential (ADP) is developed with force-matching method based on the ab initio reference data. The potential can predict the accurate properties for pure Al, such as lattice constant, elastic constants, point defects, especially the melting point. It can also ensure that the L12-Al3Zr crystal is in solid state when the Al crystal is in liquid state. The interfacial stability (work of adhesion, Wad) of Al/ L12-Al3Zr interfaces calculated with this potential agrees well with the first-principles’ results. The initial heterogeneous nucleation behavior of liquid Al on L12-Al3Zr crystal was studied with molecular dynamics based on this potential. Liquid Al atoms preferred to nucleate on the AlZr-terminated L12-Al3Zr(100) surface, due to the fact that there is only one stable adsorption site for Al atoms on this surface. The growth behavior of liquid Al atoms is decided by the orientation of L12-Al3Zr crystal surface.

Structure and thermodynamics of liquid ruthenium and ruthenium-based alloys from ab initio and classical molecular dynamics with embedded atom model potentials

The combination of classical and ab initio molecular dynamics simulations for computing structural and thermodynamic properties of metallic liquids is illustrated on the example of ruthenium and ruthenium-based alloys. The classical simulations used embedded atom model (EAM) potentials parametrized with the force matching method. The ab initio reference data were obtained using two electronic structure codes implementing the density functional theory plane wave/pseudopotential method. Several methodological aspects in the determination of structural and thermodynamic properties in the liquid phase are examined, first for pure ruthenium. The efficiency of this combined method is finally illustrated on the structure and the pressure of ternary alloys of platinum group metals of interest in the treatment of nuclear wastes.

Dipole Cooperativity and Polarization Frustration Determine the Secondary Structure Distribution of Short Alanine Peptides in Water.

The physical driving forces for secondary structure preferences of hydrated alanine peptide are investigated with B3LYP-D3(BJ) and the adaptive force matching (AFM) method. The AFM fit to the DFT surface, ALA2022, provides excellent agreement with the nuclear magnetic resonance scalar coupling constants from experiments. In turn, the model is used to gain insight into the physical driving forces behind secondary structure preferences of hydrated peptides. DFT calculations with and without the Conductor-like Screening Model (COSMO) show that the α helix is stabilized by solvent polarization due to dipole cooperativity. The two adjacent amide groups in β strand form a near-planar trapezoid that is not much larger than the size of water molecules. When the finite size of a water molecule is considered, the stabilization from solvent polarization for such a trapezoid is frustrated. Water molecules cannot find orientations to properly stabilize all four polar regions close to each other with such an awkward arrangement. This leads to quite substantial reduction in polarization stabilization. Although the polyproline II (PP-II) conformation is very similar to the β strand, the small twist in the backbone angles allowed much improved polarization stabilization. The improved polarization, when combined with favorable intrapeptide interactions, leads to the PP-II to be lowest in free energy. Other factors, such as the entropic TΔS and the ϕ, ψ coupling terms, are also studied but are found to play only a minor role. The insight shown in this work helps to better understand the structure of globular and intrinsic disordered proteins and facilitate future force field development.

An embedded-atom method potential for studying the properties of Fe-Pb solid-liquid interface

A new interatomic potential for Fe-Pb binary system is developed in the framework of an embedded atom model using the force-matching method. Compared with the ab initio calculations and experiment values, the developed Fe-Pb EAM potential can accurately describe the ground state, defects and liquid properties of crystal and Fe-Pb solid-liquid interface, such as equation of state, vacancy and interstitial formation energies, adsorption and escape energies, melting point, radial distribution function and density at high temperature. High accuracy and feasibility of the developed Fe-Pb EAM potential can provide the further reliable studies on the corrosion behavior of liquid Pb on steels used in complicate environment of the irradiation, high temperature, pressure in nuclear reactors.

Pair structure, diffusion and pressure in liquid CuZr alloys from ab initio simulations: assessing the sensitivity to the energy cutoff

An accurate determination of the liquid structure, dynamics and thermodynamics on the same footing from ab initio molecular dynamics requires particular attention in setting up the electronic structure calculation. Using two well established simulation codes implementing the density functional theory with modern projector augmented wave sets, extensive ab initio molecular dynamics runs have been performed on the CuZr liquid alloy, a prototype of glass-forming alloys. Simulation cells involving about 3000 electrons and energy cutoffs from 285 up to 640 eV, well above the values usually taken in simulations of liquid alloys have been used. The influence of the energy cutoff on structural and thermodynamic properties is examined, with a view to estimating the limiting values required for providing reliable reference data for the classical simulations with parametrized force fields. The impact on classical simulations is illustrated with optimized embedded atom model potentials using the force matching method. The various data collected confirm that the ionic pair structure and the diffusion are indeed well converged for energy cutoffs larger than about 285 eV. The greater sensitivity observed for the pressure underlines the necessity to pay more attention to the question of incomplete basis set and the structure independent electronic contributions.

Atomistic simulations of Ag\u2013Cu\u2013Sn alloys based on a new modified embedded-atom method interatomic potential

An interatomic potential for the ternary Ag–Cu–Sn system, an important material system related to the applications of lead-free solders, is developed on the basis of the second nearest-neighbor modified embedded-atom-method formalism. Potential parameters for the ternary and related binary systems are determined based on the recently improved unary description of pure Sn and the present improvements to the unary descriptions of pure Ag and Cu. To ensure the sufficient performance of atomistic simulations in various applications, the optimization of potential parameters is conducted based on the force-matching method that utilizes density functional theory predictions of energies and forces on various atomic configurations. We validate that the developed interatomic potential exhibits sufficient accuracy and transferability to various physical properties of pure metals, intermetallic compounds, solid solutions, and liquid solutions. The proposed interatomic potential can be straightforwardly used in future studies to investigate atomic-scale phenomena in soldering applications.Graphical abstract

Performing Molecular Dynamics Simulations and Computing Hydration Free Energies on the B3LYP-D3(BJ) Potential Energy Surface with Adaptive Force Matching: A Benchmark Study with Seven Alcohols and One Amine.

The potential energy surfaces at the B3LYP-D3(BJ) level for eight solutes in dilute aqueous solutions were mapped into simple pairwise additive force field expressions using the adaptive force matching (AFM) method. The quality of the fits was validated by computing the hydration free energy (HFE), enthalpy of hydration, and diffusion constant for each solute. By force matching B3LYP-D3(BJ), the predictions from the models agree with the closest experimental HFE and enthalpy of hydration within chemical accuracy. The diffusion constants from the models are also in good agreement with experimental references. The good agreement provides confidence on the quality of B3LYP-D3(BJ) in producing potential energy surfaces for thermodynamic property calculations through AFM for the molecules studied. Accurate computational predictions could potentially provide validations to experimental measurements in cases where experimental measurements from different sources do not agree.

Angular-dependent interatomic potential for large-scale atomistic simulation of iron: Development and comprehensive comparison with existing interatomic models

The development of classical interatomic potential for iron is a quite demanding task with a long history background. A new interatomic potential for simulation of iron was created with a focus on description of crystal defects properties. In contrast with previous studies, here the potential development was based on force-matching method that requires only ab initio data as reference values. To verify our model, we studied various features of body-centered-cubic iron including the properties of point defects (vacancy and self-interstitial atom), the Peierls energy barrier for dislocations (screw and mix types), and the formation energies of planar defects (surfaces, grain boundaries, and stacking fault). The verification also implies thorough comparison of a potential with 11 other interatomic potentials reported in literature. This potential correctly reproduces the largest number of iron characteristics which ensures its advantage and wider applicability range compared to the other considered classical potentials. Here application of the model is illustrated by estimation of self-diffusion coefficients and the calculation of fcc lattice properties at high temperature.

Optimized interatomic potential for atomistic simulation of Zr-Nb alloy

We present a new classical interatomic potential for a study of the binary Zr-Nb system, taking into account a wide range of the components concentrations. The potential was developed by virtue of the force-matching method that is capable of ensuring a high accuracy at the description of the complex systems containing diverse crystal phases. At simulation of pure Zr, the potential correctly describes a relative stability of Zr phases (α-Zr, β-Zr and ω-Zr) and qualitatively reproduces the right arrangement of these phases in the phase diagram. It is remarkable that β-Zr phase is found to have a dynamically unstable structure at the low temperature, in agreement with the ab initio calculations. The potential can also play a role in considering the tasks related to the crystal defects in the Zr-Nb system. In support of this statement, we show the simulation results proving adequate representation of a number of key properties of the crystal defects in Zr-Nb system. In particular, the offered potential reproduces formation/solution energies of point defects with well accuracy. To illustrate wide application possibilities for the model, we made a prediction of atomic self-diffusion and impurity diffusion in Zr and Nb. Also, the potential ensures correct description of a screw dislocation in niobium, which is a crucial point for the investigation of plasticity.

Determining the hydration free energies of selected small molecules with MP2 and local MP2 through adaptive force matching.

Force fields for seven small solute molecules, ethanol, 2-methyl-1-propanol, 2-butanol, cyclohexene, tetrahydropyran, 1,4-dioxane, and 1,4-butanediol, in dilute aqueous solutions were created with the adaptive force matching (AFM) method using MP2 or local MP2 as reference. The force fields provide a way to predict the hydration free energies (HFEs) of these molecules with only electronic structure calculations as reference. For six of the seven molecules, the predicted HFEs are in very good agreement with experiments. For 1,4-butanediol, the model created by force matching LMP2 provides a HFE that is too positive. Further investigation suggests that LMP2 may not be sufficiently accurate for computing HFEs for alcohols with AFM. Other properties, such as enthalpy of hydration, diffusion constants, and vibrational spectra, are also computed with the force field developed. The force fields developed by AFM provide a bridge for computing ensemble properties of the reference electronic structure method. With MP2 and LMP2 as reference methods, the computed properties of the small molecular solutes are found to be in good agreement with experiments.

Development and Validation of a DFT-Based Force Field for a Hydrated Homoalanine Polypeptide.

A new force field has been created for simulating hydrated alanine polypeptides using the adaptive force matching (AFM) method. Only density functional theory calculations using the Perdew–Burke–Ernzerhof exchange–correlation functional and the D3 dispersion correction were used to fit the force field. The new force field, AFM2020, predicts NMR scalar coupling constants for hydrated homopolymeric alanine in better agreements with experimental data than several other models including those fitted directly to such data. For Ala7, the new force field shows about 15% helical conformations, 20% conformation in the β basin, and 65% polyproline II. The predicted helical population of short hydrated alanine is higher than previous estimates based on the same experimental data. Gas-phase simulations indicate that the force field developed by AFM solution-phase data is likely to produce a reasonable conformation distribution when hydration water is no longer present, such as the interior of a protein.

Effects of Al on the precipitation of B2 Cu-rich particles in Fe–Cu ferritic alloy: Experimental and theoretical study

The fundamental mechanism of the precipitation kinetics and stability of nano-sized Cu-precipitates are crucial to the development of ultra-high strength low carbon ferritic steels. The effects of Al on the formation and stabilization of B2 Cu-rich precipitates in Fe–Cu based steels were studied using experimental method combining the first-principles calculations and molecular dynamics simulations. With increasing aging time, the Cu-rich particles with B2 structure precipitated in the ferritic matrix with cube-on-cube and coherent relationship, and Al addition leads to a relatively higher precipitation hardening effect. The first-principle calculations indicate that the metastable B2 FeCu phase has relatively higher mixing energy and small lattice mismatch with the ferritic matrix, and the addition of Al leads to the lower mixing energy of B2 precipitates and the B2 structure Fe(CuAl) compound possesses more smaller lattice mismatch with ferritic matrix. To better understanding the effect of Al on the evolution process of Cu-rich particles, it is essential to investigate the migration and clustering process of Cu atoms during the isothermal tempering at the atomic scale. To this end, we first developed a new interatomic potential of Fe–Cu–Al using the force-matching method based on ab initio calculations, then the formation and evolution of Cu clusters in the Fe–Cu–Al ternary were studied using molecular dynamics method with the new EAM potential. The simulation results indicate that Al addition promotes the clustering of Cu atoms due to the attractive interaction between Cu and Al atoms which enhances nucleation rate of the Cu-rich precipitates.

Optimized interatomic potential for study of structure and phase transitions in Si-Au and Si-Al systems

Metal-semiconductor nanostructures are key objects for multifunctional electronics and optical design. We report a new interatomic potential for atomistic simulation of a ternary Si-Au-Al system. The development procedure was based on the force-matching method that allowed us to create the potential without use of experimental data at the fitting. Extensive validation including elastic, thermophysical and defect properties demonstrates a wide range of the potential applicability. Special attention was paid to the description of the silicon-metal alloys in liquid and amorphous states. We used the new potential for study of crystallization and glass transition in the undercooled melt. The simulation results revealed the beneficial conditions for the formation of the unique metal-semiconductor nanocrystalline structure, which is highly important for various applications in the field of nanophotonics.

Development of a Polarizable Interatomic Potential for Molten Lithium, Sodium, and Potassium Nitrate.

A polarizable interatomic potential is developed for atomistic simulations of molten MNO3 (M = Li, Na, K) salts. The potential is parametrized using a force matching method relying on the adjustment of parameters such that density functional theory generated forces, stress tensors, and dipole moments are reproduced. Simulations conducted using the new potential are used to estimate physical parameters of the melt, which are then compared with available experimental results. The average calculated densities of NaNO3 and KNO3 are within 2% of the experimental value within the temperature range studied, while that of LiNO3 is within 3%. Thermal conductivities and viscosities are estimated using equilibrium calculations and the Green-Kubo method. The thermal conductivity values of NaNO3 and KNO3 are found to match well with experimental data, while that of LiNO3 is approximately 20% larger than experimentally determined values throughout the temperature ranges simulated. The calculated viscosities are also in good agreement with experimentally determined values. The (NaxK1-x)NO3 mixture is also investigated, with densities, thermal conductivities, and viscosities determined and compared with experimentally determined values where available. Additionally, radial and angular distribution function data is presented for all salts, revealing details of the atom-level structures present in the melts. We have found that the new interatomic potential is effective for atom scale modeling of the physical properties of molten nitrate salts.

Analytically Predicating the Multi-Dimensional Accuracy of the Honed Engine Cylinder Bore

Abstract The dimensional accuracy of engine cylinder bore at multiscale has a tremendous influence on engine performances including friction power loss, vibration, leak tightness between piston and cylinder, and wear resistance. Tremendous researches were devoted to predict the dimensional accuracies of the honed cylinder by means of analytical, experimental, and numerical simulation methods. The dimensional quality of the honed cylinder bore was usually determined by establishing the relationship between honing parameters and dimensional accuracies of the honed cylinder bore. However, most researches predicted dimensional accuracy at macroscale or surface texture at microscale, respectively. Few efforts were devoted to predict the dimensional quality of honed cylinder bore at both macroscale and microscale levels simultaneously. To explore a new understanding of the honing mechanism of the cylinder bore, a multiscale model is proposed to predict the dimensional accuracy and surface texture of cylinder bore generated from the honing process at the macroscale and microscale simultaneously. The model aims to integrate both microscale factors including honing stone abrasives distribution, abrasive wear process, previous cylinder surface topography, and macroscale factors including cylinder geometric features and honing head motion trajectory into a multiscale analytical analysis. A force matching method is adopted in the multiscale predictive model to determine the feed depth in the honing of the cylinder bore. Thus, the proposed multiscale analytical model possesses an excellent capacity to simultaneously predict the roundness and cylindricity of the honed cylinder bore, as well as the surface texture/roughness of the honed cylinder bore in terms of Abbott-Firestone curve. The simulated results also revealed that the material removal process is closely related to the initial shape deviations of the cylinder bore, which cannot be corrected, compensated, or eliminated by the subsequent honing process given the deviations are associated with wavelengths higher than 27 mm under the given honing condition.

Extension of the force-matching method to coarse-grained models with axially symmetric sites to produce transferable force fields: Application to the UNRES model of proteins.

The force-matching approach to coarse graining, in which the forces that act on site centers are fitted to the respective average forces computed from all-atom molecular dynamics simulations, provides a link between coarse-grained and all-atom molecular dynamics. In the existing implementations, radial site-site interaction potentials are assumed, thus precluding extensive coarse-graining that usually requires anisotropic potentials. In this work, we extended the force-matching approach to coarse-grained models with axially symmetric sites and implemented it to the UNRES model of polypeptide chains developed in our laboratory, in which the only interaction sites are united peptide groups and united side chains, the α-carbon atoms serving as anchor points. The optimizable parameters were those of the UNRES energy function and not whole potential profiles, which provide better transferability. We tested the implementation with the 20-residue tryptophan-cage miniprotein, selected as the training protein, starting from the NEWCT-9P variant of UNRES. The reference forces were obtained from implicit- and explicit-solvent simulations. Using a target function composed of a force-matching term and a maximum-likelihood term that drives the force field at reproducing the NMR-determined conformational ensembles at three selected temperatures, force fields were obtained which did not produce site-site clashes for the structures simulated with all-atom molecular dynamics with AMBER, and modeled the structures of α-helical proteins with resolution comparable to that of the NEWCT-9P force field. The new force fields also produced the free-energy landscapes of tryptophan cage similar to those obtained from the all-atom molecular dynamics runs.

Study of the transient dynamics of coarse-grained molecular systems with the path-space force-matching method

Molecular dynamics simulations is a field of science that studies interactions of atoms at a very small order of magnitude. The difficulties due to the enormous range of length and time scales, lead us to average out the details of the atomistic level, to the molecular level. Such a dimensionality reduction method is called coarse-graining. In this work, we apply the path-space force matching method for coarse-graining at transient and equilibrium dynamics regimes. We derive time-dependent representations of the coarse particle interactions and verify that they reduce to the potential of mean force, as time increases. We validate the performance of the path-space force matching through the study of a benchmark molecular system.